Overclock the hell out of the x4 965 BE and the 7850. Both are capable of being pushed hard.
Throw out the ssd if the budget is too high. But, keep it if you can, as it'll make a difference.
Find good deals. The prices in the list below may not be the cheapest.
PCPartPicker part list: http://pcpartpicker.com/p/yd59
Price breakdown by merchant: http://pcpartpicker.com/p/yd59/by_merchant/
CPU: AMD Phenom II X4 965 Black 3.4GHz Quad-Core Processor ($89.99 @ NCIX US)
CPU Cooler: Cooler Master Hyper 212 EVO 82.9 CFM Sleeve Bearing CPU Cooler ($24.99 @ Newegg)
Motherboard: Asus M5A97 ATX AM3+ Motherboard ($99.98 @ PCM)
Memory: Samsung 8GB (2 x 4GB) DDR3-1600 Memory ($44.99 @ Newegg)
Storage: Kingston SSDNow V200 Series 64GB 2.5" Solid State Disk ($52.99 @ Newegg)
Video Card: HIS Radeon HD 7850 2GB Video Card ($206.98 @ Newegg)
Power Supply: Corsair Builder 500W 80 PLUS Bronze Certified ATX12V Power Supply ($51.98 @ Newegg)
(Prices include shipping, taxes, and discounts when available.)
(Generated by PCPartPicker 2013-01-18 02:51 EST-0500)